Question 1

Given the probability distribution: $$x = 1, P(x) = 0.12; x = 2, P(x) = 0.09; x = 3, P(x) = 0.73; x = 4, P(x) = 0.02; x = 5, P(x) = ?. $$What is the missing probability $$P(x=5)$$?

Accepted Answer

$$P(x=5) = 0.04$$

Question 2

Using the probability distribution above, what is the probability that $$x is $$more than 2?

Accepted Answer

$$P(x \u003e 2) = 0.79$$

Question 3

For the roulette game: A player bets $$5 on slot #17 (probability of winning $$\frac{1}{38}$$). If the ball lands on #17, the player wins 175$$; otherwise, loses $5. What is the expected value of the player's winnings?

Accepted Answer

$$E = -\0.13$

Question 4

In a sample of 30 teenagers, 70% had MP3 players by age 16. What is the probability that exactly 18 had MP3 players by age 16? (Use binomial formula: $$P(X=k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$)

Accepted Answer

$$P(X=18) \approx 0.23$$

Question 5

A sample of 450 bananas has a 6% chance of being overripe. What is the mean and standard deviation for the number of overripe bananas? (Use $$\mu = np$$, $$\sigma = \sqrt{np(1-p)})$$

Accepted Answer

$$\mu = 27, \sigma \approx 5.03$$

Question 6

A produce manager found 35 overripe bananas in a sample of 450. Is this unusual? (Mean $$=27$$, SD $$\approx 5.03)$$

Accepted Answer

Yes, because $$35 is $$more than $$1.5$$ standard deviations above the mean.

Question 7

Which of the following is a binomial experiment?

Accepted Answer

Polling 100 registered voters about their opinion on Social Security reform.

Question 8

Find the z-score so that the area under the standard normal curve to its right is $$0.1056. ($$Use $$P(Z \u003e z) = 0.1056)$$

Accepted Answer

Question 9

Find the z-score so that the area under the standard normal curve to its left is $$0.2655. ($$Use $$P(Z \u003c z) = 0.2655)$$

Accepted Answer

$$z \approx -0.62$$

Question 10

Find the z-scores that separate the middle 10% of the standard normal curve.

Accepted Answer

$$z \approx -1.645$$ and $$z \approx 1.645$$

Question 11

Find the area under the standard normal curve to the right of $$z = -1.36.$$

Accepted Answer

$$0.9131$$

Question 12

Find the area under the standard normal curve to the left of $$z = 2.34.$$

Accepted Answer

$$0.9904$$

Question 13

The salaries for full-time PhD students are normally distributed with mean $$\12$$,837$$ and standard deviation $$\$$1,500. $$What is the probability that a randomly selected student earns more than $$\15$$,000$?

Accepted Answer

$$P \approx 0.0668$$

Question 14

If a group of 50 graduate students is selected, what is the probability that their average salary is more than $$\15$$,000$$? (Use Central Limit Theorem: $$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$)

Accepted Answer

$$P \approx 0.0000$$

Question 15

To qualify for a job at a health club, candidates must score in the upper 40% on a fitness test. The test has a mean of $$200$$ and a standard deviation of $$20. $$What is the lowest qualifying score?

Accepted Answer

$$210$$

Question 16

In a binomial experiment with $$n=30$$ and $$p=0.7$$, what is the probability that at least 14 had MP3 players by age 16?

Accepted Answer

$$P(X \geq 14) \approx 0.99$$

Question 17

In the probability distribution, what is the mean $$\mu$$? (Use $$\mu = \sum x P(x))$$

Accepted Answer

$$\mu = 3.02$$

Question 18

In the probability distribution, what is the standard deviation $$\sigma$$? (Use $$\sigma = \sqrt{\sum (x - \mu)^2$ P(x)})$$

Accepted Answer

$$\sigma \approx 0.77$$

Question 19

In a sample of 450 bananas, what is the probability that less than 17 are overripe? (Use normal approximation to binomial)

Accepted Answer

$$P \approx 0.0228$$

Step-by-Step Guidance for Introductory Statistics Practice Problems (Chapters 6–8)

Study Guide - Practice Questions

Study Guide - Flashcards